Fourier Layer

Fourier layers are increasingly used in neural networks to leverage the efficiency and properties of the Fourier transform for various tasks. Current research focuses on developing Fourier-based architectures, such as Fourier neural operators and modified MLPs, that are equivariant to transformations like rotations and translations, and that can handle varying resolutions or sparse data, particularly for solving partial differential equations and image processing problems. This approach offers advantages in terms of computational efficiency, improved generalization across different scales and resolutions, and enhanced interpretability by incorporating physical constraints or filtering out domain-specific information. The resulting models show promise for applications ranging from fluid dynamics simulations to image deblurring and domain generalization in machine learning.